Question

2. According to a study done by Pew Research Center, 37% of adult Americans believe that marriage is now obsolete. Suppose a random sample of 180 Americans is asked whether marriage is obsolete. What is the probability that more than 30% believe that marriage is obsolete? Use 4 non-zero decimal places in your calculations. Round z-values to 2 decimal places.

Answer 1

Solution

Given that,

p = 0.37

1 - p = 1-0.37=0.63

n = 180

= p =0.37

=  [p ( 1 - p ) / n] =   [(0.37*0.63) / 180 ] = 0.03599

P( <0.30 ) =

= P[( - ) / < (0.30-0.37) / 0.03599]

= P(z <-1.94 )

Using z table,   

probability =0.0262